What is a 'derivative'?

If we have a function f(x), taking its derivative would obtain a new function f'(x). However, now this second function f'(x) defines the tangent along any point on the original graph of f(x). This is useful for an astonishing amount of areas of mathematics, and it is important you know some of them to fully comprehend why it is we study differential equations/derivatives.

AP

Related Maths A Level answers

All answers ▸

Express the following as a partial fraction: (4x^2+12x+9) / (x^2+3x+2) .


In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50 and angle BCA= x Find the two possible values for x, giving your answers to one decimal place.


At time t = 0, a particle is projected vertically upwards with speed u m s–1 from a point 10 m above the ground. At time T seconds, the particle hits the ground with speed 17.5 m s–1. Find the value of u and T and evaluate the model. (AS mechanics)


Let f(x) and g(x) be two odd functions defined for all real values of x. Given that s(x)=f(x)+g(x), prove that s(x) is also an odd function.